Performance limitations in sensitivity reduction for nonlinear plants

This paper investigates performance limitations imposed by 'non-minimum phase' characteristics of a nonlineaR time-varying plant. A performance criterion is defined which, in the linear case, is analogous to minimizing the sensitivity over a given frequency band. It is shown that if the nonlinear plant is 'non-minimum phase', then the frequency-weighted sensitivity cannot be made arbitrarily small while keeping the overall sensitivity bounded. The non-minimum phasedness of the plant is stated in terms of a deficiency in its range. These results extend the familiar 'push/pop' phenomenon in sensitivity optimization to a nonlinear time-varying setting.